Bart Haegeman

Diversity-dependence brings molecular phylogenies closer to agreement with the fossil record

The branching times of molecular phylogenies allow us to infer speciation and extinction dynamics even when fossils are absent. Troublingly, phylogenetic approaches usually return estimates of zero extinction, conflicting with fossil evidence. Phylogenies and fossils do agree, however, that there are often limits to diversity. Here, we present a general approach to evaluate the likelihood of a phylogeny under a model that accommodates diversity-dependence and extinction. We find, by likelihood maximization, that extinction is estimated most precisely if the rate of increase in the number of lineages in the phylogeny saturates towards the present or first decreases and then increases. We demonstrate the utility and limits of our approach by applying it to the phylogenies for two cases where a fossil record exists (Cetacea and Cenozoic macroperforate planktonic foraminifera) and to three radiations lacking fossil evidence (Dendroica, Plethodon and Heliconius). We propose that the diversity-dependence model with extinction be used as the standard model for macro-evolutionary dynamics because of its biological realism and flexibility.

Robust estimation of microbial diversity in theory and in practice.

Quantifying diversity is of central importance for the study of structure, function and evolution of microbial communities. The estimation of microbial diversity has received renewed attention with the advent of large-scale metagenomic studies. Here, we consider what the diversity observed in a sample tells us about the diversity of the community being sampled. First, we argue that one cannot reliably estimate the absolute and relative number of microbial species present in a community without making unsupported assumptions about species abundance distributions. The reason for this is that sample data do not contain information about the number of rare species in the tail of species abundance distributions. We illustrate the difficulty in comparing species richness estimates by applying Chao’s estimator of species richness to a set of in silico communities: they are ranked incorrectly in the presence of large numbers of rare species. Next, we extend our analysis to a general family of diversity metrics (‘Hill diversities’), and construct lower and upper estimates of diversity values consistent with the sample data. The theory generalizes Chao’s estimator, which we retrieve as the lower estimate of species richness. We show that Shannon and Simpson diversity can be robustly estimated for the in silico communities. We analyze nine metagenomic data sets from a wide range of environments, and show that our findings are relevant for empirically-sampled communities. Hence, we recommend the use of Shannon and Simpson diversity rather than species richness in efforts to quantify and compare microbial diversity.

A Conceptual and Statistical Framework for Adaptive Radiations with a Key Role for Diversity Dependence

In this article we propose a new framework for studying adaptive radiations in the context of diversity-dependent diversification. Diversity dependence causes diversification to decelerate at the end of an adaptive radiation but also plays a key role in the initial pulse of diversification. In particular, key innovations (which in our definition include novel traits as well as new environments) may cause decoupling of the diversity-dependent dynamics of the innovative clade from the diversity-dependent dynamics of its ancestral clade. We present a likelihood-based inference method to test for decoupling of diversity dependence using molecular phylogenies. The method, which can handle incomplete phylogenies, identifies when the decoupling took place and which diversification parameters are affected. We illustrate our approach by applying it to the molecular phylogeny of the North American clade of the legume tribe Psoraleeae (47 extant species, of which 4 are missing). Two diversification rate shifts were previously identified for this clade; our analysis shows that the first, positive shift can be associated with decoupling of two Pediomelum subgenera from the other Psoraleeae lineages, while we argue that the second, negative shift can be attributed to speciation being protracted. The latter explanation yields nonzero extinction rates, in contrast to previous findings. Our framework offers a new perspective on macroevolution: new environments and novel traits (ecological opportunity) and diversity dependence (ecological limits) cannot be considered separately.

A mathematical synthesis of niche and neutral theories in community ecology

The debate between niche-based and neutral community theories centers around the question of which forces shape predominantly ecological communities. Niche theory attributes a central role to niche differences between species, which generate a difference between the strength of intra- and interspecific interactions. Neutral theory attributes a central role to migration processes and demographic stochasticity. One possibility to bridge these two theories is to combine them in a common mathematical framework. Here we propose a mathematical model that integrates the two perspectives. From a niche-based perspective, our model can be interpreted as a Lotka-Volterra model with symmetric interactions in which we introduce immigration and demographic stochasticity. From a neutral perspective, it can be interpreted as Hubbells local community model in which we introduce a difference between intra- and interspecific interactions. We investigate the stationary species abundance distribution and other community properties as functions of the interaction coefficient, the immigration rate and the strength of demographic stochasticity.

Genomic fluidity: an integrative view of gene diversity within microbial populations

BackgroundThe dual concepts of pan and core genomes have been widely adopted as means to assess the distribution of gene families within microbial species and genera. The core genome is the set of genes shared by a group of organisms; the pan genome is the set of all genes seen in any of these organisms. A variety of methods have provided drastically different estimates of the sizes of pan and core genomes from sequenced representatives of the same groups of bacteria.ResultsWe use a combination of mathematical, statistical and computational methods to show that current predictions of pan and core genome sizes may have no correspondence to true values. Pan and core genome size estimates are problematic because they depend on the estimation of the occurrence of rare genes and genomes, respectively, which are difficult to estimate precisely because they are rare. Instead, we introduce and evaluate a robust metric - genomic fluidity - to categorize the gene-level similarity among groups of sequenced isolates. Genomic fluidity is a measure of the dissimilarity of genomes evaluated at the gene level.ConclusionsThe genomic fluidity of a population can be estimated accurately given a small number of sequenced genomes. Further, the genomic fluidity of groups of organisms can be compared robustly despite variation in algorithms used to identify genes and their homologs. As such, we recommend that genomic fluidity be used in place of pan and core genome size estimates when assessing gene diversity within genomes of a species or a group of closely related organisms.

The neutral theory of biodiversity with random fission speciation

The neutral theory of biodiversity and biogeography emphasizes the importance of dispersal and speciation to macro-ecological diversity patterns. While the influence of dispersal has been studied quite extensively, the effect of speciation has not received much attention, even though it was already claimed at an early stage of neutral theory development that the mode of speciation would leave a signature on metacommunity structure. Here, we derive analytical expressions for the distribution of abundances according to the neutral model with recruitment (i.e., dispersal and establishment) limitation and random fission speciation which seems to be a more realistic description of (allopatric) speciation than the point mutation mode of speciation mostly used in neutral models. We find that the two modes of speciation behave qualitatively differently except when recruitment is strongly limited. Fitting the model to six large tropical tree data sets, we show that it performs worse than the original neutral model with point mutation speciation but yields more realistic predictions for speciation rates, species longevities, and rare species. Interestingly, we find that the metacommunity abundance distribution under random fission is identical to the broken-stick abundance distribution and thus provides a dynamical explanation for this grand old lady of abundance distributions.

Relaxing the zero-sum assumption in neutral biodiversity theory

The zero-sum assumption is one of the ingredients of the standard neutral model of biodiversity by Hubbell. It states that the community is saturated all the time, which in this model means that the total number of individuals in the community is constant over time, and therefore introduces a coupling between species abundances. It was shown recently that a neutral model with independent species, and thus without any coupling between species abundances, has the same sampling formula (given a fixed number of individuals in the sample) as the standard model [Etienne, R.S., Alonso, D., McKane, A.J., 2007. The zero-sum assumption in neutral biodiversity theory. J. Theor. Biol. 248, 522-536]. The equilibria of both models are therefore equivalent from a practical point of view. Here we show that this equivalence can be extended to a class of neutral models with density-dependence on the community-level. This result can be interpreted as robustness of the model, i.e. insensitivity of the model to the precise interaction of the species in a neutral community. It can also be interpreted as a lack of resolution, as different mechanisms of interactions between neutral species cannot be distinguished using only a single snapshot of species abundance data.

Entropy Maximization and the Spatial Distribution of Species

Entropy maximization (EM, also known as MaxEnt) is a general inference procedure that originated in statistical mechanics. It has been applied recently to predict ecological patterns, such as species abundance distributions and species‐area relationships. It is well known in physics that the EM result strongly depends on how elementary configurations are described. Here we argue that the same issue is also of crucial importance for EM applications in ecology. To illustrate this, we focus on the EM prediction of species‐level spatial abundance distributions. We show that the EM outcome depends on (1) the choice of configuration set, (2) the way constraints are imposed, and (3) the scale on which the EM procedure is applied. By varying these choices in the EM model, we obtain a large range of EM predictions. Interestingly, they correspond to spatial abundance distributions that have been derived previously from mechanistic models. We argue that the appropriate choice of the EM model assumptions is nontrivial and can be determined only by comparison with empirical data.

Resilience, reactivity and variability: A mathematical comparison of ecological stability measures.

In theoretical studies, the most commonly used measure of ecological stability is resilience: ecosystems asymptotic rate of return to equilibrium after a pulse-perturbation -or shock. A complementary notion of growing popularity is reactivity: the strongest initial response to shocks. On the other hand, empirical stability is often quantified as the inverse of temporal variability, directly estimated on data, and reflecting ecosystems response to persistent and erratic environmental disturbances. It is unclear whether and how this empirical measure is related to resilience and reactivity. Here, we establish a connection by introducing two variability-based stability measures belonging to the theoretical realm of resilience and reactivity. We call them intrinsic, stochastic and deterministic invariability; respectively defined as the inverse of the strongest stationary response to white-noise and to single-frequency perturbations. We prove that they predict ecosystems worst response to broad classes of disturbances, including realistic models of environmental fluctuations. We show that they are intermediate measures between resilience and reactivity and that, although defined with respect to persistent perturbations, they can be related to the whole transient regime following a shock, making them more integrative notions than reactivity and resilience. We argue that invariability measures constitute a stepping stone, and discuss the challenges ahead to further unify theoretical and empirical approaches to stability.

General relationships between consumer dispersal, resource dispersal and metacommunity diversity

One of the central questions of metacommunity theory is how dispersal of organisms affects species diversity. Here, we show that the diversity-dispersal relationship should not be studied in isolation of other abiotic and biotic flows in the metacommunity. We study a mechanistic metacommunity model in which consumer species compete for an abiotic or biotic resource. We consider both consumer species specialised to a habitat patch, and generalist species capable of using the resource throughout the metacommunity. We present analytical results for different limiting values of consumer dispersal and resource dispersal, and complement these results with simulations for intermediate dispersal values. Our analysis reveals generic patterns for the combined effects of consumer and resource dispersal on the metacommunity diversity of consumer species, and shows that hump-shaped relationships between local diversity and dispersal are not universal. Diversity-dispersal relationships can also be monotonically increasing or multimodal. Our work is a new step towards a general theory of metacommunity diversity integrating dispersal at multiple trophic levels.